How to model this branched sculpture?
You could definitely use Dynamic Topology (Dyntopo) and get something like that with the Snake Hook brush.

Start with a primitive like a cube or sphere.
Switch to Sculpt Mode.
Press CtrlD to toggle on Dyntopo or enable it in: Tool Shelf > Tools > Dyntopo.



If you decide to use Dynamic Topology then there is no need to use a Multiresolution Modifier. As you sculpt, topology will be created or tessellated dynamically where it is needed.
Begin roughing in your shapes with a high Detail size (Maximum Edge Length) and then gradually work towards a smaller Detail pixel setting (Zooming in and out also affects detail size). The hotkey for the Detail size is ShiftD.
In the Detail Refine Method, choose Subdivide Collapse method when using the Snake Hook Brush. Make sure to lower your Detail so that the extrusion doesn't break apart. 

Retopology will need to be performed after using this method. Note: Dyntopo will destroy custom data layers such as UVs or Vertex colors attached to the mesh. Also, anytime that you leave sculpt mode (going into Edit Mode for example) will turn off Dyntopo. 

Consider the following workflow: 


Dyntopo to create the base model
Retopologize mesh
Multiresolution Modifier Sculpting in incremental levels to add in final detail to the mesh.